The fact that a disordered complex structure, that is apparently
random in nature, allows an ordered substructure is not
the result of Chaos Theory but rather of Ramsey's Theory. In a most
explicit manner the latter theory asserts that there lies a substructure
possessing a given property within all sufficiently large structures. It
is clear that the sufficient condition regarding the structure's height
is always fulfilled within the situations where Chaos Theory is
applicable.

Chaotic behaviour within a system displays delicate sensitivity to
tiny changes in such a manner that any ignorance of its present state
leads to complete ignorance concerning its state after a brief period of
time, for example, weather prediction is affected by this problem. Order
develops on a large scale through the concatenation of several
small-scale events on the verge of instability. In 1961 the metereologist
Lorenz accidentally discovered the butterfly effect, whereby the
movement of a butterfly's wing(s) taking place today in one part of the
world brings about an extremely small change in the state of the
atmosphere which can have radical repercussions on global weather
patterns.

In Lorenz's words; the butterfly effect is the phenomenon that a
small alteration in the state (the condition of a system at one instant)
of a dynamical or deterministic system (a system in which later states
evolve from previous ones according to a fixed law) will cause subsequent
states to differ greatly from the states that would have followed without
the alteration. Lorenz referred to this cumulative effect as sensitive
dependence. After a certain length of time the atmosphere's behaviour
diverges from the expected behaviour. Lorenz published his seminal
article in 1963, wherein he referred to the possibility of long-term
weather forecasting via the prediction or estimation of its periodic
variations. Lorenz lent his name to the Lorenz Attractor: in other
words,chaotic motion in a dissipative(volume-decreasing) system.

Currently, it is possible to perform a conveyance of frame and to
apply this approach to the generation of an idea in the brain or
encephalon. Within this materialistic context, where thought is
considered to be like an emergence of cerebral activity, each idea would
involve the activation of a series of neurones that constitute a fractal
trajectory within the topological space represented by the brain.

The simplest form of 'fractal' objects (a
concept introduced by Benoit Mandelbrot in 1975) are self-similar or
self-affine. In other words, these fractals do not
change their appearance when viewed under a microscope of arbitrary
magnifying power. Natural boundaries such as coast lines apparently
become longer the finer the scale on which we measure them. One of the
characteristics of the boundary is its self-similarity, also known as
Julia Sets. In 1980 Mandelbrot discovered what was later to be termed the
Mandelbrot Set, with its associated spiral-like peninsula on its edge.
The term 'multifractality' was first coined by Mandelbrot. Therefore, it
would be theoretically possible to attribute a fractal dimension to an
idea in order to distinguish it from white noise. Consequently, within
this framework thought would be made up of a succession of deterministic
ideas developing within a chaotic environment or milieu.

The computation of the fractal dimension of an irregular
phenomenon such as an idea (within consecutive bursts of cerebral
activity arising due to successive deterministic synaptic-neuronal
activation processes) depends on several factors. One critical factor
that comes into play and that stands out over and above the background
white noise concerns the competing neurotransmitted signals within the
chaotic, quasi-random milieu of the mind. The human brain's potential
electrical and neurochemical transmission relies heavily upon "encephalic
goodness", i.e. neuronal efficiency, to the extent that a finite number
of cerebral signals will trigger off appropriate brain responses during
the complex process of thought generation, hence giving rise to the
emergent property of human conscience and awareness.

First of all, it is necessary to bring to light the fact that
the deterministic view can indeed be identified as it is the brain's normal
functioning mode. So, without doubt, in order to resolve this problem and
therby extract the information concerning an idea's fractal dimension it
will be necessary to make use of the wavelet multifractal approach. In
the end, the study of the fractal spectrum, obtained with the aid of
wavelets, will enable the separation which is associated with human
thought.

Human thought can be abstracted as the end product of a finite
series of "stochastic" processes involving very swift and oscillating,
bidirectional exchanges between cerebral areas of low and high entropy,
thereby epitomizing the idea of structure or order within chaos.The
fractal dimensionality of thought, as derived from Chaos Theory, is
postulated on the basis of the nesting of an apparently random set of
cerebral events within the ordered framework of a neurologically and
topologically defined, finite brain architecture. There exists an
'apparent random' connection of a huge number of neurones creating an
almost infinite number of possible permutations and combinations, but
this is all based on a few 'rules' laid down by the human genetic code
that manages to govern how body cells should connect and
interact.

The following is a paradigm of a deterministic structure
comprising a nondeterministic substructure : the prime numbers and the
classes 4n+3 and 4n+1. The set of prime numbers is deterministic in the
sense that via elliptical curves one can give a
certification of the primality of a number. In
addition, if we consider the difference between the numbers of prime
numbers of the class 4n+3 and those of 4n+1, we can demonstrate that it
changes sign an infinite number of times. Nevertheless, it remains
positive over extremely long ranges. It is the sign of this difference
that constitutes a nondeterministic object within the deterministic
structure of prime numbers.

This paradigm shows that the nesting of determinism and
indeterminism is dual. Chaos and order can be found to coexist in a type
of competitive symbiosis. This result is altogether typical within the
framework of a fractal mentality since it highlights the complexity of
the notion of boundary. Complex adaptive systems thrive in the hinterland
between the inflexibilities of classical determinism and the vagaries of
chaos. The theory of Laplace's Classical Determinism can be applied to
diverse chaotic systems such as; a snowflake, a time series with its
random walk, a pinball machine, and Hyperion's almost random oscillations
along its own axes with respect to its eccentric, elliptical orbit around
Saturn. These stable systems allow stable predictions to be made.
Thought pattern generation is unlikely to be a phenomenon involving
similar stability in terms of experimental test and retest verification.

The aforegoing consolidates the idea that the interaction between
phenomena of low and high entropy is not a problem but rather a reality
which should be taken into account. It can be concluded that the
specifics of the qualitative and quantitative interactions that take
place within the brain and along the brainstem still remain to be
elucidated.